In the circuit on the right, is the unknown resistance to be measured; , and are resistors of known resistance and the resistance of is adjustable. If the ratio of the two resistances in the known leg is equal to the ratio of the two in the unknown leg , then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer . is varied until this condition is reached. The current direction indicates whether is too high or too low.
Detecting zero current can be done to extremely high accuracy (see galvanometer). Therefore, if , and are known to high precision, then can be measured to high precision. Very small changes in disrupt the balance and are readily detected.
At the point of balance, the ratio of
Alternatively, if , , and are known, but is not adjustable, the voltage or current flow through the meter can be used to calculate the value of , using Kirchhoff's circuit laws (also known as Kirchhoff's rules). This setup is frequently used in strain gauge and Resistance Temperature Detector measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.
First, Kirchhoff's first rule is used to find the currents in junctions B and D: : :
Then, Kirchhoff's second rule is used for finding the voltage in the loops ABD and BCD:
The bridge is balanced and , so the second set of equations can be rewritten as:
Then, the equations are divided and rearranged, giving:
From the first rule, and . The desired value of is now known to be given as:
If all four resistor values and the supply voltage () are known, the voltage across the bridge () can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is:
This can be simplified to:
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